Polytope of Type {9,14}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9,14}*1764
if this polytope has a name.
Group : SmallGroup(1764,66)
Rank : 3
Schlafli Type : {9,14}
Number of vertices, edges, etc : 63, 441, 98
Order of s0s1s2 : 18
Order of s0s1s2s1 : 14
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {3,14}*588
49-fold quotients : {9,2}*36
147-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 36)( 3, 22)( 4, 8)( 5, 43)( 6, 29)( 7, 15)( 9, 39)( 10, 25)
( 12, 46)( 13, 32)( 14, 18)( 16, 42)( 17, 28)( 19, 49)( 20, 35)( 23, 38)
( 26, 45)( 27, 31)( 30, 41)( 33, 48)( 40, 44)( 50, 99)( 51,134)( 52,120)
( 53,106)( 54,141)( 55,127)( 56,113)( 57,102)( 58,137)( 59,123)( 60,109)
( 61,144)( 62,130)( 63,116)( 64,105)( 65,140)( 66,126)( 67,112)( 68,147)
( 69,133)( 70,119)( 71,101)( 72,136)( 73,122)( 74,108)( 75,143)( 76,129)
( 77,115)( 78,104)( 79,139)( 80,125)( 81,111)( 82,146)( 83,132)( 84,118)
( 85,100)( 86,135)( 87,121)( 88,107)( 89,142)( 90,128)( 91,114)( 92,103)
( 93,138)( 94,124)( 95,110)( 96,145)( 97,131)( 98,117)(148,393)(149,428)
(150,414)(151,400)(152,435)(153,421)(154,407)(155,396)(156,431)(157,417)
(158,403)(159,438)(160,424)(161,410)(162,399)(163,434)(164,420)(165,406)
(166,441)(167,427)(168,413)(169,395)(170,430)(171,416)(172,402)(173,437)
(174,423)(175,409)(176,398)(177,433)(178,419)(179,405)(180,440)(181,426)
(182,412)(183,394)(184,429)(185,415)(186,401)(187,436)(188,422)(189,408)
(190,397)(191,432)(192,418)(193,404)(194,439)(195,425)(196,411)(197,344)
(198,379)(199,365)(200,351)(201,386)(202,372)(203,358)(204,347)(205,382)
(206,368)(207,354)(208,389)(209,375)(210,361)(211,350)(212,385)(213,371)
(214,357)(215,392)(216,378)(217,364)(218,346)(219,381)(220,367)(221,353)
(222,388)(223,374)(224,360)(225,349)(226,384)(227,370)(228,356)(229,391)
(230,377)(231,363)(232,345)(233,380)(234,366)(235,352)(236,387)(237,373)
(238,359)(239,348)(240,383)(241,369)(242,355)(243,390)(244,376)(245,362)
(246,295)(247,330)(248,316)(249,302)(250,337)(251,323)(252,309)(253,298)
(254,333)(255,319)(256,305)(257,340)(258,326)(259,312)(260,301)(261,336)
(262,322)(263,308)(264,343)(265,329)(266,315)(267,297)(268,332)(269,318)
(270,304)(271,339)(272,325)(273,311)(274,300)(275,335)(276,321)(277,307)
(278,342)(279,328)(280,314)(281,296)(282,331)(283,317)(284,303)(285,338)
(286,324)(287,310)(288,299)(289,334)(290,320)(291,306)(292,341)(293,327)
(294,313);;
s1 := ( 1,148)( 2,190)( 3,183)( 4,176)( 5,169)( 6,162)( 7,155)( 8,154)
( 9,196)( 10,189)( 11,182)( 12,175)( 13,168)( 14,161)( 15,153)( 16,195)
( 17,188)( 18,181)( 19,174)( 20,167)( 21,160)( 22,152)( 23,194)( 24,187)
( 25,180)( 26,173)( 27,166)( 28,159)( 29,151)( 30,193)( 31,186)( 32,179)
( 33,172)( 34,165)( 35,158)( 36,150)( 37,192)( 38,185)( 39,178)( 40,171)
( 41,164)( 42,157)( 43,149)( 44,191)( 45,184)( 46,177)( 47,170)( 48,163)
( 49,156)( 50,246)( 51,288)( 52,281)( 53,274)( 54,267)( 55,260)( 56,253)
( 57,252)( 58,294)( 59,287)( 60,280)( 61,273)( 62,266)( 63,259)( 64,251)
( 65,293)( 66,286)( 67,279)( 68,272)( 69,265)( 70,258)( 71,250)( 72,292)
( 73,285)( 74,278)( 75,271)( 76,264)( 77,257)( 78,249)( 79,291)( 80,284)
( 81,277)( 82,270)( 83,263)( 84,256)( 85,248)( 86,290)( 87,283)( 88,276)
( 89,269)( 90,262)( 91,255)( 92,247)( 93,289)( 94,282)( 95,275)( 96,268)
( 97,261)( 98,254)( 99,197)(100,239)(101,232)(102,225)(103,218)(104,211)
(105,204)(106,203)(107,245)(108,238)(109,231)(110,224)(111,217)(112,210)
(113,202)(114,244)(115,237)(116,230)(117,223)(118,216)(119,209)(120,201)
(121,243)(122,236)(123,229)(124,222)(125,215)(126,208)(127,200)(128,242)
(129,235)(130,228)(131,221)(132,214)(133,207)(134,199)(135,241)(136,234)
(137,227)(138,220)(139,213)(140,206)(141,198)(142,240)(143,233)(144,226)
(145,219)(146,212)(147,205)(295,393)(296,435)(297,428)(298,421)(299,414)
(300,407)(301,400)(302,399)(303,441)(304,434)(305,427)(306,420)(307,413)
(308,406)(309,398)(310,440)(311,433)(312,426)(313,419)(314,412)(315,405)
(316,397)(317,439)(318,432)(319,425)(320,418)(321,411)(322,404)(323,396)
(324,438)(325,431)(326,424)(327,417)(328,410)(329,403)(330,395)(331,437)
(332,430)(333,423)(334,416)(335,409)(336,402)(337,394)(338,436)(339,429)
(340,422)(341,415)(342,408)(343,401)(345,386)(346,379)(347,372)(348,365)
(349,358)(350,351)(352,392)(353,385)(354,378)(355,371)(356,364)(359,391)
(360,384)(361,377)(362,370)(366,390)(367,383)(368,376)(373,389)(374,382)
(380,388);;
s2 := ( 1, 11)( 2, 10)( 3, 9)( 4, 8)( 5, 14)( 6, 13)( 7, 12)( 15, 46)
( 16, 45)( 17, 44)( 18, 43)( 19, 49)( 20, 48)( 21, 47)( 22, 39)( 23, 38)
( 24, 37)( 25, 36)( 26, 42)( 27, 41)( 28, 40)( 29, 32)( 30, 31)( 33, 35)
( 50, 60)( 51, 59)( 52, 58)( 53, 57)( 54, 63)( 55, 62)( 56, 61)( 64, 95)
( 65, 94)( 66, 93)( 67, 92)( 68, 98)( 69, 97)( 70, 96)( 71, 88)( 72, 87)
( 73, 86)( 74, 85)( 75, 91)( 76, 90)( 77, 89)( 78, 81)( 79, 80)( 82, 84)
( 99,109)(100,108)(101,107)(102,106)(103,112)(104,111)(105,110)(113,144)
(114,143)(115,142)(116,141)(117,147)(118,146)(119,145)(120,137)(121,136)
(122,135)(123,134)(124,140)(125,139)(126,138)(127,130)(128,129)(131,133)
(148,158)(149,157)(150,156)(151,155)(152,161)(153,160)(154,159)(162,193)
(163,192)(164,191)(165,190)(166,196)(167,195)(168,194)(169,186)(170,185)
(171,184)(172,183)(173,189)(174,188)(175,187)(176,179)(177,178)(180,182)
(197,207)(198,206)(199,205)(200,204)(201,210)(202,209)(203,208)(211,242)
(212,241)(213,240)(214,239)(215,245)(216,244)(217,243)(218,235)(219,234)
(220,233)(221,232)(222,238)(223,237)(224,236)(225,228)(226,227)(229,231)
(246,256)(247,255)(248,254)(249,253)(250,259)(251,258)(252,257)(260,291)
(261,290)(262,289)(263,288)(264,294)(265,293)(266,292)(267,284)(268,283)
(269,282)(270,281)(271,287)(272,286)(273,285)(274,277)(275,276)(278,280)
(295,305)(296,304)(297,303)(298,302)(299,308)(300,307)(301,306)(309,340)
(310,339)(311,338)(312,337)(313,343)(314,342)(315,341)(316,333)(317,332)
(318,331)(319,330)(320,336)(321,335)(322,334)(323,326)(324,325)(327,329)
(344,354)(345,353)(346,352)(347,351)(348,357)(349,356)(350,355)(358,389)
(359,388)(360,387)(361,386)(362,392)(363,391)(364,390)(365,382)(366,381)
(367,380)(368,379)(369,385)(370,384)(371,383)(372,375)(373,374)(376,378)
(393,403)(394,402)(395,401)(396,400)(397,406)(398,405)(399,404)(407,438)
(408,437)(409,436)(410,435)(411,441)(412,440)(413,439)(414,431)(415,430)
(416,429)(417,428)(418,434)(419,433)(420,432)(421,424)(422,423)(425,427);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s0*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(441)!( 2, 36)( 3, 22)( 4, 8)( 5, 43)( 6, 29)( 7, 15)( 9, 39)
( 10, 25)( 12, 46)( 13, 32)( 14, 18)( 16, 42)( 17, 28)( 19, 49)( 20, 35)
( 23, 38)( 26, 45)( 27, 31)( 30, 41)( 33, 48)( 40, 44)( 50, 99)( 51,134)
( 52,120)( 53,106)( 54,141)( 55,127)( 56,113)( 57,102)( 58,137)( 59,123)
( 60,109)( 61,144)( 62,130)( 63,116)( 64,105)( 65,140)( 66,126)( 67,112)
( 68,147)( 69,133)( 70,119)( 71,101)( 72,136)( 73,122)( 74,108)( 75,143)
( 76,129)( 77,115)( 78,104)( 79,139)( 80,125)( 81,111)( 82,146)( 83,132)
( 84,118)( 85,100)( 86,135)( 87,121)( 88,107)( 89,142)( 90,128)( 91,114)
( 92,103)( 93,138)( 94,124)( 95,110)( 96,145)( 97,131)( 98,117)(148,393)
(149,428)(150,414)(151,400)(152,435)(153,421)(154,407)(155,396)(156,431)
(157,417)(158,403)(159,438)(160,424)(161,410)(162,399)(163,434)(164,420)
(165,406)(166,441)(167,427)(168,413)(169,395)(170,430)(171,416)(172,402)
(173,437)(174,423)(175,409)(176,398)(177,433)(178,419)(179,405)(180,440)
(181,426)(182,412)(183,394)(184,429)(185,415)(186,401)(187,436)(188,422)
(189,408)(190,397)(191,432)(192,418)(193,404)(194,439)(195,425)(196,411)
(197,344)(198,379)(199,365)(200,351)(201,386)(202,372)(203,358)(204,347)
(205,382)(206,368)(207,354)(208,389)(209,375)(210,361)(211,350)(212,385)
(213,371)(214,357)(215,392)(216,378)(217,364)(218,346)(219,381)(220,367)
(221,353)(222,388)(223,374)(224,360)(225,349)(226,384)(227,370)(228,356)
(229,391)(230,377)(231,363)(232,345)(233,380)(234,366)(235,352)(236,387)
(237,373)(238,359)(239,348)(240,383)(241,369)(242,355)(243,390)(244,376)
(245,362)(246,295)(247,330)(248,316)(249,302)(250,337)(251,323)(252,309)
(253,298)(254,333)(255,319)(256,305)(257,340)(258,326)(259,312)(260,301)
(261,336)(262,322)(263,308)(264,343)(265,329)(266,315)(267,297)(268,332)
(269,318)(270,304)(271,339)(272,325)(273,311)(274,300)(275,335)(276,321)
(277,307)(278,342)(279,328)(280,314)(281,296)(282,331)(283,317)(284,303)
(285,338)(286,324)(287,310)(288,299)(289,334)(290,320)(291,306)(292,341)
(293,327)(294,313);
s1 := Sym(441)!( 1,148)( 2,190)( 3,183)( 4,176)( 5,169)( 6,162)( 7,155)
( 8,154)( 9,196)( 10,189)( 11,182)( 12,175)( 13,168)( 14,161)( 15,153)
( 16,195)( 17,188)( 18,181)( 19,174)( 20,167)( 21,160)( 22,152)( 23,194)
( 24,187)( 25,180)( 26,173)( 27,166)( 28,159)( 29,151)( 30,193)( 31,186)
( 32,179)( 33,172)( 34,165)( 35,158)( 36,150)( 37,192)( 38,185)( 39,178)
( 40,171)( 41,164)( 42,157)( 43,149)( 44,191)( 45,184)( 46,177)( 47,170)
( 48,163)( 49,156)( 50,246)( 51,288)( 52,281)( 53,274)( 54,267)( 55,260)
( 56,253)( 57,252)( 58,294)( 59,287)( 60,280)( 61,273)( 62,266)( 63,259)
( 64,251)( 65,293)( 66,286)( 67,279)( 68,272)( 69,265)( 70,258)( 71,250)
( 72,292)( 73,285)( 74,278)( 75,271)( 76,264)( 77,257)( 78,249)( 79,291)
( 80,284)( 81,277)( 82,270)( 83,263)( 84,256)( 85,248)( 86,290)( 87,283)
( 88,276)( 89,269)( 90,262)( 91,255)( 92,247)( 93,289)( 94,282)( 95,275)
( 96,268)( 97,261)( 98,254)( 99,197)(100,239)(101,232)(102,225)(103,218)
(104,211)(105,204)(106,203)(107,245)(108,238)(109,231)(110,224)(111,217)
(112,210)(113,202)(114,244)(115,237)(116,230)(117,223)(118,216)(119,209)
(120,201)(121,243)(122,236)(123,229)(124,222)(125,215)(126,208)(127,200)
(128,242)(129,235)(130,228)(131,221)(132,214)(133,207)(134,199)(135,241)
(136,234)(137,227)(138,220)(139,213)(140,206)(141,198)(142,240)(143,233)
(144,226)(145,219)(146,212)(147,205)(295,393)(296,435)(297,428)(298,421)
(299,414)(300,407)(301,400)(302,399)(303,441)(304,434)(305,427)(306,420)
(307,413)(308,406)(309,398)(310,440)(311,433)(312,426)(313,419)(314,412)
(315,405)(316,397)(317,439)(318,432)(319,425)(320,418)(321,411)(322,404)
(323,396)(324,438)(325,431)(326,424)(327,417)(328,410)(329,403)(330,395)
(331,437)(332,430)(333,423)(334,416)(335,409)(336,402)(337,394)(338,436)
(339,429)(340,422)(341,415)(342,408)(343,401)(345,386)(346,379)(347,372)
(348,365)(349,358)(350,351)(352,392)(353,385)(354,378)(355,371)(356,364)
(359,391)(360,384)(361,377)(362,370)(366,390)(367,383)(368,376)(373,389)
(374,382)(380,388);
s2 := Sym(441)!( 1, 11)( 2, 10)( 3, 9)( 4, 8)( 5, 14)( 6, 13)( 7, 12)
( 15, 46)( 16, 45)( 17, 44)( 18, 43)( 19, 49)( 20, 48)( 21, 47)( 22, 39)
( 23, 38)( 24, 37)( 25, 36)( 26, 42)( 27, 41)( 28, 40)( 29, 32)( 30, 31)
( 33, 35)( 50, 60)( 51, 59)( 52, 58)( 53, 57)( 54, 63)( 55, 62)( 56, 61)
( 64, 95)( 65, 94)( 66, 93)( 67, 92)( 68, 98)( 69, 97)( 70, 96)( 71, 88)
( 72, 87)( 73, 86)( 74, 85)( 75, 91)( 76, 90)( 77, 89)( 78, 81)( 79, 80)
( 82, 84)( 99,109)(100,108)(101,107)(102,106)(103,112)(104,111)(105,110)
(113,144)(114,143)(115,142)(116,141)(117,147)(118,146)(119,145)(120,137)
(121,136)(122,135)(123,134)(124,140)(125,139)(126,138)(127,130)(128,129)
(131,133)(148,158)(149,157)(150,156)(151,155)(152,161)(153,160)(154,159)
(162,193)(163,192)(164,191)(165,190)(166,196)(167,195)(168,194)(169,186)
(170,185)(171,184)(172,183)(173,189)(174,188)(175,187)(176,179)(177,178)
(180,182)(197,207)(198,206)(199,205)(200,204)(201,210)(202,209)(203,208)
(211,242)(212,241)(213,240)(214,239)(215,245)(216,244)(217,243)(218,235)
(219,234)(220,233)(221,232)(222,238)(223,237)(224,236)(225,228)(226,227)
(229,231)(246,256)(247,255)(248,254)(249,253)(250,259)(251,258)(252,257)
(260,291)(261,290)(262,289)(263,288)(264,294)(265,293)(266,292)(267,284)
(268,283)(269,282)(270,281)(271,287)(272,286)(273,285)(274,277)(275,276)
(278,280)(295,305)(296,304)(297,303)(298,302)(299,308)(300,307)(301,306)
(309,340)(310,339)(311,338)(312,337)(313,343)(314,342)(315,341)(316,333)
(317,332)(318,331)(319,330)(320,336)(321,335)(322,334)(323,326)(324,325)
(327,329)(344,354)(345,353)(346,352)(347,351)(348,357)(349,356)(350,355)
(358,389)(359,388)(360,387)(361,386)(362,392)(363,391)(364,390)(365,382)
(366,381)(367,380)(368,379)(369,385)(370,384)(371,383)(372,375)(373,374)
(376,378)(393,403)(394,402)(395,401)(396,400)(397,406)(398,405)(399,404)
(407,438)(408,437)(409,436)(410,435)(411,441)(412,440)(413,439)(414,431)
(415,430)(416,429)(417,428)(418,434)(419,433)(420,432)(421,424)(422,423)
(425,427);
poly := sub<Sym(441)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s0*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope